Relativistic many-body theory of finite nuclei and the Schwinger-Dyson formalism

A method is shown to derive a consistent Hamiltonian of nucleon and meson system in a finite nucleus from a Lorentz-scalar Lagrangian. For this purpose, the Schwinger-Dyson method is applied to a many-body problem of the interacting nucleons and mesons in a finite system. Using this method, closed equations of exact Green’s functions for single-particle motions of a nucleon and a meson are derived. It is shown that the interactions of nucleons and mesons generate local dependent potentials in a finite system and that the potentials can be determined self-consistently on the basis of the many-body Schwinger-Dyson formalism. In the method, condensed meson fields are extracted from the meson fields and treated as c-number fields, so that the classical equations of the condensed fields become equivalent to those of the mean-field theory originally proposed by Walecka et al.$-— The present method is regarded as a natural extension of mean-field theory to a full quantum treatment for finite systems. The method provides a self-consistent description of the single-particle motions of nucleons and mesons and their mutual interactions. It allows us to include full quantum effects and to describe not only the ground state but also excited states in a systematic way.